Multilevel selection in the evolution of sexual dimorphism in phenotypic plasticity

Phenotypes are partly shaped by the environment, which can impact bothshort-term adaptation and long-term evolution. In dioecious species, thetwo sexes may exhibit different degrees of phenotypic plasticity and theor-etical models indicate that such differences may confer an adaptiveadvantage when the population is subject to directional selection, eitherbecause of a systematically varying environment or a load of deleteriousmutations. The effect stems from the fundamental asymmetry between thetwo sexes: female fertility is more limited than male fertility. Whether thisasymmetry is sufficient for sexual dimorphism in phenotypic plasticity toevolve is, however, not obvious. Here, we show that even in conditionswhere it provides an adaptive advantage, dimorphic phenotypic plasticitymay be evolutionarily unstable due to sexual selection. This is the case, inparticular, for panmictic populations where mating partnerships areformed at random. However, we show that the effects of sexual selectioncan be counteracted when mating occurs within groups of related individ-uals. Under this condition, sexual dimorphism in phenotypic plasticity cannot only evolve but offset the twofold cost of males. We demonstrate thesepoints with a simple mathematical model through a combination of analyti-cal and numerical results.